Let ABC, PQR be two congruent triangles such that angle A = angle P = 90°. If BC = 13cm, PR = 5cm, find AB.

Correct option is A

​Given:
- $$\triangle ABC$$ and  $$\triangle PQR$$​ are congruent right-angled triangles.
-  $$\angle A = \angle P = 90^\circ$$​
- Hypotenuse   BC = 13 cm 
- Side PR = 5cm 
Theorem  Used:
- Pythagoras theorem:

$$\text{In a right-angled triangle, } \text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2$$​​
Solution:

​
Since $$\triangle ABC \ and \ \triangle PQR$$​ are congruent, corresponding sides are equal. So,  BC = QR = 13 cm  and  PR = AB 

Applying the Pythagoras theorem in $$\triangle PQR$$​:

​$$QR^2 = PQ^2 + PR^2$$​​
Substitute the known values:
​$$13^2 = PQ^2 + 5^2$$​​
​$$169 = PQ^2 + 25$$​​
​$$PQ^2 = 169 - 25 = 144$$​​
​$$PQ = \sqrt{144} = 12$$​​
Therefore,  AB = 12 cm